Polarisation Extension for confocal microscope attoCFM I

Polarisation Extension for confocal microscope attoCFM I
Polarization extension for the confocal microscope attoCFM I
by
Daniel Stroh
A Master Thesis submitted to the Department of Applied Sciences and Mechatronics
University of Applied Sciences, Munich
Major Subject: Photonics
Approved:
_____________________________________________
Prof. Dr. rer. nat. Rolf Heilmann, Thesis Adviser
_____________________________________________
Prof. Dr. rer. nat. Manfred Fickenscher, Second Adviser
Munich, 2013
CONTENTS
LIST OF FIGURES .......................................................................................................... iii
ABSTRACT .......................................................................................................................v
ABSTRAKT ..................................................................................................................... vi
1. Introduction ..................................................................................................................1
2. Theory...........................................................................................................................3
2.1
Confocal microscopy ..........................................................................................3
2.2
Polarization theory and components ...................................................................5
2.2.1
State of polarization ................................................................................5
2.2.2
Jones vector representation .....................................................................6
2.2.3
Methods of modifying polarization and phase........................................7
3. Setup ...........................................................................................................................11
3.1
Idealized schematic ...........................................................................................11
3.2
Integration capability into attoCFM I ...............................................................13
3.3
Final setup .........................................................................................................14
3.4
3.3.1
Setup design ..........................................................................................14
3.3.2
Choice of components...........................................................................17
Alignment procedure ........................................................................................20
3.4.1
Collimation of beam .............................................................................20
3.4.2
Laser coupling .......................................................................................23
3.5
Working procedure: Gain maximum Extinction Ratio .....................................24
3.6
Determination of polarization axis....................................................................26
3.7
Transmission .....................................................................................................27
3.7.1
Coupling efficiency for collimated beam .............................................27
3.7.2
Other transmission results .....................................................................28
3.8
Angular resolution of polarizer .........................................................................29
3.9
Influence of beam splitter .................................................................................30
4. Results ........................................................................................................................32
4.1
4.2
Extinction Ratio ................................................................................................32
4.1.1
Influence of QWP and LCVR ...............................................................34
4.1.2
Influence of vacuum window................................................................35
4.1.3
Spatial filter ...........................................................................................36
Mode Imaging ...................................................................................................39
i
4.3
Angular sensitivity of a mirror / Focus shift .................................................... 40
4.4
Stability ............................................................................................................ 46
5. Summary .................................................................................................................... 49
BIBLIOGRAPHY ............................................................................................................ 51
ACKNOWLEDGMENT .................................................................................................. 53
ii
LIST OF FIGURES
Figure 2.1 Schematic principle of confocal microscopy [4]. ..................................................... 4
Figure 2.2 Various waves for different phase delays Γ [8]. ....................................................... 6
Figure 2.3 Circlular porazied electromagentic wave with the field vector E0 in the direction of
propagation axis –z [4]. .................................................................................................. 6
Figure 2.4 Transmission of unpolarized incident light through a pair of Polaroids with their
transmission axes forming an angle θ. The arrows with the solid heads indicate the
electric vectors at each step [11]..................................................................................... 8
Figure 2.5 Separation of ordinary and extraordinary rays in passing through a sheet of calcite
[11]. ................................................................................................................................ 9
Figure 2.6 Types of liquid crystals. (a) Cholestric crystal; (b) Smectic liquid crystal; (c)
Nematic liquid crystal; (d) Discotic liquid crystal in nematic-like orientation [14]. ... 10
Figure 3.1 Idealized schematic. ................................................................................................ 11
Figure 3.2 Idealized schmetaic including functional components (QWP, tunable retarder). ... 12
Figure 3.3 attoCFM I design. ................................................................................................... 13
Figure 3.4 Breadboard copy of the CFM head. ........................................................................ 14
Figure 3.5 First general design following attoCFM I integration guidelines. .......................... 15
Figure 3.6 Complete setup with highlighted blocks/arms and optional Inspection optics. ...... 15
Figure 3.7 Finding the best design with a PowerPoint template. ............................................. 16
Figure 3.8 Top view of one setup. Red line indicates the excitation, green line the detection
ray path. ........................................................................................................................ 17
Figure 3.9 LPVIS Series Transmission and Extinction Ratio .................................................. 18
Figure 3.10 Beam splitter BSS11 transmission. ....................................................................... 18
Figure 3.11 Liquid crystal variable retarder (LCVR) in rotation cage plate. ........................... 19
Figure 3.12 Wave plate performance. ...................................................................................... 20
Figure 3.13 Confocal setup for objective adjustment and mirror alignment for excitation and
detection arm. ............................................................................................................... 21
Figure 3.14 Development of two focused points at positions f and f' > f................................. 21
Figure 3.15 Principle of beam walking using two mirrors M1, M2, one iris diaphragm and an
alignment disk. ............................................................................................................. 22
Figure 3.16 Setup with fixed components and optional inspection optics. .............................. 22
Figure 3.17 Laser coupling unit inside box. ............................................................................. 23
Figure 3.18 Schematic of the laser source and additional excitation arm for the alignment
process. ......................................................................................................................... 24
Figure 3.19 First simplified setup schematic including both polarizers P1, P2 and the high-NA
objective. Excitation and detection arm are comprised in X and D. ............................ 25
Figure 3.20 Pattern for optimizing extinction ratio ER. ........................................................... 25
Figure 3.21 Configuration to determine the polarization axis. ................................................. 26
Figure 3.22 Setup for measuring the coupling efficiency of the excitation and detection arm.
(a) Measurement of U(FC/PC); (b) measurement of U(x,PC) ..................................... 28
Figure 3.23 Mathematical angular resolution requirement. (a) f(θ) = cos²(θ), linear scale; (b)
f(θ) = cos²(θ), logarithmic y-axis; (c) f(θ) = cos²(θ); logarithmic y-axis, zoomed in. .. 29
iii
Figure 3.24 Influence of beam splitter on throughput. .............................................................30
Figure 3.25 Optical properties of the beam splitter BSS11. (a) Transmission; (b)
Reflectance. ...................................................................................................................31
Figure 4.1 First setup to determine ER without the beam splitter. ...........................................32
Figure 4.2 Summary of different configurations and according range of extinction ratios on
the right. (a) Polarizer P1 and analyzer P2; (b) both polarizers P1, P2 and sample
objective; (c) both polarizers P1, P2, sample objective and different beam splitter. ....33
Figure 4.3 Extinction ratio as a function of the polarizer angle. ...............................................34
Figure 4.4 Simplified setup to determine influence of (a) QWP and (b) ER increase with
LCVR. ...........................................................................................................................34
Figure 4.5 Setup to determine the influence of the vacuum window. ......................................35
Figure 4.6 Extinction ratio at different vacuum window positions...........................................36
Figure 4.7 Vacuum window positions according to the orienation of the E-vector to the
window. .........................................................................................................................36
Figure 4.8 Simplified setup to image different modes of the fiber and test a different sized
pinhole by replacing the SM-fiber with a MM-fiber. ...................................................37
Figure 4.9 Mode dependence at two different wavelengths (635 nm, 905 nm) and comparison
with a multimode fiber. The average ER is stated above every mode image. ..............38
Figure 4.10 Mode imaging of the free beam after the analyzer. (a) Setup; (b) Captured mode
with lobe pattern............................................................................................................39
Figure 4.11 Mode imaging of the free beam after the analyzer with an imaging lens. (a) Setup;
(b) Cross-polarized; (c) Co-polarized. ..........................................................................39
Figure 4.12 Evolution of lobe-pattern dpending on the rotation angle of the poalizer P1........40
Figure 4.13 Schematic of mirror tilt represented by the change in angle α caused by the
displacement x from the µm screw at the top. ..............................................................41
Figure 4.14 Sample screenshot and description of the setup for determing the angular
sensitivity of the mirror. ................................................................................................41
Figure 4.15 Schematic drawing of the resulting focus shift after the objective, due to mirror
tilt. .................................................................................................................................42
Figure 4.16 Visual description of rotation terms at the example of the beam shape with sample
objective. .......................................................................................................................42
Figure 4.17 Comparison of normalized maximum power and extinction ratio to focus shift
and mirror tilt for a setup without sample objective for different axes; (a) Yaw axis;
(b) Pitch Axis; (c) Yaw + pitch axis. ............................................................................44
Figure 4.18 Comparison of normalized maximum power and extinction ratio to focus shift
and mirror tilt for a setup with high-NA sample objective for different axes; (a) Yaw
axis; (b) Pitch Axis; (c) Yaw + pitch axis. ....................................................................45
Figure 4.19 Simplified setup for long-term stability test. .........................................................46
Figure 4.20 Long-term stability, with sample objective. ..........................................................46
Figure 4.21 Long-term pointing stability without sample objective. Polarizer and analyzer are
in vertical position. The detected voltage is normalized. ..............................................47
Figure 4.22 Long-term stability with beam splitter cube, extra 5 m patch cord cable, no
sample objective. Highest extinction ratio of >1E8. .....................................................48
iv
ABSTRACT
Cross-polarization is an efficient method for resonance fluorescence measurements done in
quantum research. The study of quantum dots and nano structures opens the door to quantum
computing. The goal of this project is to extend the existing confocal microscope attoCFM I
from attocube, with the ability to perform cross-polarization measurements that achieve an
extinction ratio of the excitation laser beam of at least 1×106. This was already achieved in a
laboratory at the LMU München with the previous version of the confocal microscope. A
schematic copy of the new attoCFM I is set up on a breadboard using the same parts as
applicable. All necessary components, like the beam splitter, coupling units, quarter wave plate
and tunable retarder are characterized and discussed. Different configurations are tested to
ensure the required extinction ratio and gain knowledge about the setup. Support is given by
thorough procedures to facilitate the project hand-over.
v
ABSTRAKT
Cross-polarization stellt eine effiziente Methode zur Messung der resonanten Fluoreszenz mit
einem konfokalen Mikroskop in der Quantenmechanik dar. Die Forschung an quantum dots
und nano Strukturen öffnet die Türen zu Quantenrechnern. Das Ziel dieser Arbeit ist das
bestehende konfokale Mikroskop attoCFM I von attocube so zu erweitern, dass es möglich ist
cross-polarization Messungen durchzuführen, die eine Unterdrückung des Anregungslasers um
den Extinktionsfaktor 1×106 erreicht. Das wurde bereits in einem Forschungslabor an der LMÜ
München mit dem Vorgängermodell des konfokalen Mikroskops erreicht. Eine schematische
Kopie des neuen attoCFM I wird aufgebaut, die möglichst die gleichen Teile verwendet. Alle
notwendigen Komponenten, wie der Strahlteiler, Koppeleinheiten, Lamda/4-Platte und
verstellbarer Phasenverzögerer werden charakterisiert und diskutiert. Unterschiedliche
Konfigurationen werden untersucht, um die geforderte Extinktionsrate immer zu gewährleisten
und Erfahrung zu sammeln. Sorgfältige Anleitungen sollen die Projektübergabe nach Abschluss
der Thesis erleichtern.
vi
1. Introduction
1. Introduction
Further developments in material science and life sciences, especially biological and
medical studies, require higher resolutions and an extended portfolio on measurement
techniques. The wide commercial availability and advances of confocal microscopes make this
technique very attractive in research. It allows for noninvasive 3D investigation of a specimen
and even in vivo experiments. A niche market is found in resonance fluorescence and quantum
dot measurements. One technique, like the single-molecule fluorescence-excitation
spectroscopy, detects broad Stokes-shifted fluorescence by filtering out light at the excitation
wavelength from the laser on a very low background. However, it does not provide information
on the coherence of the molecular transition. Two other experiments use the interference
between the excitation laser beam and the scattered light from the molecule, but require 100,000
photons for the detection of 1 particular emission, which is time consuming. The fast detection
of a coherently driven emission is the major goal in the research on nonlinear interactions
between single emitters and photons. A cross-polarized configuration of a confocal microscope
is able to suppress a high amount of the excitation in order to detect single emissions at the
same wavelength from the probe in a fraction of time compared to other methods[1]. Single and
biexcitation quantum dot transitions were observed with resonant excitation and detected with
a cross-polarized confocal microscope setup. This allows for more research in quantum
information processing [2].
The successful polarization extension of the previous confocal microscope from attocube
proves the feasibility of this method in the group of Alex Högele at the LMU München. In
combination with the demand for this type of research, it is desirable to offer a commercialized
product. The main task of this project is to create a breadboard setup that achieves an extinction
of the excitation laser by a ratio of at least 1×106. The configuration is highly adapted to the
latest version of the confocal microscope attoCFM I and uses the same components, as they are
applicable. It comprises a fiber coupled excitation and detection unit, a mirror representing the
sample unit and a combining beam splitter. Two linear thin-film polarizers are rotated with their
polarization axes perpendicular to each other and the suppressed power monitored. The setup
is tested on efficiency and different configurations. The influence from the quarter wave plate,
the beam splitter and other optical or mechanical components is discussed. A method for
improving the extinction with the introduction of a tunable retarder is examined. The
requirement of single-mode fibers, that act as pinholes in the confocal configuration, is
analyzed. Further free-beam images visualize the impact of the high-NA sample objective on
the mode. A thorough investigation of the angular mirror tilt provides information about the
mechanical requirement and connected focus shift on the fiber and the effect of the sample
objective on the detection. A final stability study investigates further configuration changes and
the long-term behaviour of the system.
1
1. Introduction
Throughout the whole project, emphasis is put on the documentation and reliability of the
collected data and drawn conclusions. Therefore, a working procedure describes how to achieve
a high extinction ratio. Another alignment procedure explains the effective collimation of a
laser beam and the coupling of the laser. The intention of the thesis is to offer a comprehensible
report and provide repeatable processes for the continuation and further development of the
product. The experience drawn during this project is of great importance for the next steps, like
integration into the attoCFM I design and sample measurements.
2
2. Theory
2. Theory
2.1 Confocal microscopy
Confocal microscopy gained attraction mainly in the biological and medical field for its
outstanding capabilities of studying microscopic systems at the frontier of the diffraction limit.
It achieves this important goal by making use of a scanning approach together with a confocal
optical system. Traditional wide-field microscopes image an entire object and thus are limited
by the wavelength of the used light and numerical aperture of the optics. The resolution in the
direction of the optical axis is related to the depth of field, which depends on the size of the
imaged structure. Fine image detail, which is generally of most interest, has a small depth of
field and only features within a small distance of the focal plane contribute to the image. By
removing the out-of-focus light, a confocal system improves the fidelity of focal sectioning and
increases the contrast in image details [3]. The schematic configuration consists of a light
source, in this case a laser for higher intensity, which is focused on an aperture B1 that passes
the beam splitter BS and is then focused on the z = z0 plane of the object with the objective lens
L2. Backscattered light is collected from the sample and imaged after the beam splitter on the
pinhole B2. Light from other planes different from z0 is blocked by the aperture B2, thus
leading to a decrease in intensity on the detector [4].
A fiber-coupled configuration, as it is realized in the attoCFM I, uses a collimated beam to
increase the efficiency and collect as much light as possible. The fiber core acts as the pinhole
and only light within its numerical aperture NA is captured. In order to increase the collection
of the emission of the object it is beneficial to use a high-NA sample objective. Again, only the
light from the focal point is imaged on the fiber core and the sample cannot be displayed
entirely. Therefore, it is scanned on a xyz-translation stage to cover the desired surface and
create a three-dimensional image.
Like a conventional optical microscope, the resolution of a confocal microscope is limited
by the diffraction of light. The image of an ideal point viewed through a circular aperture is
blurred, and the diffracted image is known as the Airy disc. The size of the Airy disc depends
on the wavelength of the laser source and the numerical aperture of the objective lens. This Airy
disc limits the maximum resolution of the microscope in the sample plane due to the Rayleigh
criterion, which states that two Airy discs must be separated by at least their radius in order to
3
2. Theory
Detector
B2
Laser
BS
L1
B1
z
y
L2
x
z = z0
z < z0
Object
Figure 2.1 Schematic principle of confocal microscopy [4].
be resolved [5]. The radius of a Gaussian beam is defined as the radius where the electric field
has dropped to 1/e of its maximum value in the center of the beam. The beam waist, defined as
the radius of the beam in the focus, is w0 and the divergence angle is θ. The radius of the
Gaussian beam as a function of z is then given by
 z 
r  w0 1  
2 
  w0 
2
(1.1)
The Rayleigh length zR is the distance where the beam waist is increased by √2. The Rayleigh
range gives an approximate dividing line between the near-field and the far-field for a focussed
Gaussian beam. For 𝑧 ≫ 𝑧𝑅 the beam radius follows the linear divergence
r
z
 z
 w0
(1.2)
with the divergence angle θ


 w0
(1.3)
For small angles θ ≈ sin(θ) and with n = 1, the numerical aperture NA = n sin(θ) is connected
through equation (1.2) to the radius of the spot for an ideal lens that focusses a Gaussian beam
4
2. Theory
to its diffraction-limited spot. That is because NA is the half angle of the light cone exiting a
lens that is illuminated with a plane wave. In order to create a particularly small spot it is
advantageous using microscope objectives over simple lenses because of their diminished level
of spherical aberration [6].
2.2 Polarization theory and components
Polarization control and understanding is crucial for many applications aiming for high
performance like material processing [7] or performance improvement on a general
experimental setup. Characteristics such as reflectivity, insertion loss, and beam splitter ratios
will be different for different polarizations. This chapter concentrates on the general
understanding and practical application of polarization control, because no measurements are
conducted to quantify or determine the exact state of polarization in this thesis.
2.2.1
State of polarization
The electric and magnetic field vectors of a plane electromagnetic (EM) wave lie in a plane
transverse to the direction of propagation. If the electric field varies randomly with time, then
the wave is said to be unpolarized, while if it varies in a predictable manner, the wave is said to
be polarized. The nature of variation of the electric field with time defines the state of
polarization (SOP) of the EM wave. Three basic, different types of polarization are
distinguished, depending on the propagation of the electrical field vector E in space, which
consists of the orthogonal components Ex and Ey
E  Ex cos t  kz   E y cos t  kz 
(1.4)
where 𝜔 = 2𝜋𝑐 ⁄𝜆 is the angular frequency of the wave, k its propagation constant and c the
speed of light. The magnitudes are given by Ex  E cos  and E y  E cos  . For a linearly
polarized wave, Ex and Ey are in phase with each other and form a straight line on the plane of
propagation [8].
If the apex of the electric vector moves on a circle, the polarization state is called circular. Such
a wave can be expressed as a superposition of two orthogonal and linearly polarized
components with equal amplitudes but having a phase difference of π/2 [9]
E  Ex cos t   E y sin t 
(1.5)
The most general SOP is the elliptical polarization. Ex and Ey are different in magnitude and
phase. Here, the tip of the electric field vector moves on an ellipse. It has the form
E  Ex cos t   E y cos t   
(1.6)
where Γ is the phase delay or phase difference between the two linear wave components. Figure
2.2 shows various waves for different phase delays Γ.
5
2. Theory
Figure 2.2 Various waves for different phase delays Γ [8].
One can think of the linear and circular polarization as a special form of the elliptical
polarization. There are different ways of generating a specific SOP from unpolarized light.
2.2.2 Jones vector representation
One method of mathematically describing the SOP is with Jones vectors. One can extend
equation (1.4) to a matrix representation and describe it as a column vector with complex
electric field vectors Ex and Ey
i
 Ex   E0 x e x 
E 

i y


E
E
e
y
   0y

(1.7)
where the phase is given by 𝜑 = 𝜔𝑡. Another graph showing a circular polarized wave with the
construction of the electric field vector based on the jones representation is shown in Figure
2.3.
Figure 2.3 Circlular porazied electromagentic wave with the field vector E0 in the direction of propagation
axis –z [4].
The normalized form of the Jones vector is defined as
i
 J x  1  E0 x e x 
J   

i y
 J y  E  E0 y e 
6
(1.8)
2. Theory
with |E| = √𝐸𝑥2 + 𝐸𝑦2 .
One can calculate the Jones vector for a linear polarized beam that has no phase difference,
𝜑𝑥 = 𝜑𝑦 , where E is pointing at angle υ on the x-axis, and with 𝐸𝑥 = 𝐸 cos 𝜗 and
𝐸𝑦 = 𝐸 sin 𝜗 as
 cos  
(1.9)
J    

 sin  
A special form of linear polarization depends on what component of E is polarized or
1
suppressed. With 𝐸𝑦 = 0 one gets horizontal linear polarization in the form of J h    and
0
accordingly vertical linear polarization, if the x component 𝐸𝑥 = 0 with the Jones matrix
0
J v    [4]. In general, many forms of polarization can be described with Jones matrices. It
1
presents a convenient and fast method of calculating various SOP.
2.2.3
Methods of modifying polarization and phase
Dichroism describes the absorption of the electric field vector E, which is orthogonal to the
transmission axis (TA) of an anisotropic material and transmission of E that is parallel to the
TA. This material is then called dichroic. After unpolarized light passes a polarizing sheet, the
polarizer, with its transmission axes at an angle θ, the outcome is a linear polarized electric field
vector at angle θ. One can place a second polarizing sheet, the analyzer, to investigate the SOP
as it is shown in Figure 2.4.
Commercial Polaroid sheets achieve a transmittance in one sense of polarization of 50%
and 1×10-4 for the orthogonal orientation. More robust dichroic filters made of glass are needed
to survive high power laser beams. The relation between transmitted intensity I of a linear
polarized beam and angle θ is described by the Malus law
I  I 0 cos2 
(1.10)
where I0 is the intensity incident on the analyzer. This law provides a quantitative resolution
requirement discussed in chapter 3.8. If the incident beam is not linearly polarized, one has to
separate the components perpendicular and parallel to the polarization axis [10].
7
2. Theory
Figure 2.4 Transmission of unpolarized incident light through a pair of Polaroids with their transmission
axes forming an angle θ. The arrows with the solid heads indicate the electric vectors at each step [11].
The extinction ratio (ER) is defined as the ratio between maximum power Pmax for the
throughput, where the transmission axis of the polarizer and analyser are parallel to each other,
and the minimum power Pmin at suppressing configuration, with their transmission axes
perpendicular to each other
U max
Pmax
gainmax
ER 

Pmin U min
gainmin
(1.11)
where gainmax and gainmin are the detector gain settings. The spectral response of the detector
can be neglected, because the factor can be reduced by it. Besides this nomenclature, one can
find the term contrast to describe the ratio between the highest and lowest power throughput of
a system. The contrast is defined as the inverse of the extinction ratio. This thesis will only use
the term extinction ratio to reduce confusion and facilitate the comparison of results.
Besides using dichroic material, it is possible to manipulate the SOP with birefringent
components. When an unpolarized light beam enters an anisotropic medium, like calcite, it
splits into two linearly polarized beams. This phenomenon is due to the interaction of an
electromagnetic wave on a dielectric medium. Incident unpolarized light can be split up to two
polarized parts, with their polarization axes perpendicular to each other. The part, which is
perpendicular to the plane of incidence, formed by the normal of the dielectric medium and the
propagation axis of the beam, is called s-polarized or a transverse electric (TE) wave. It is
usually expressed as a circle with a dot inside, implying “coming out” of the plane. The other
part is parallel to the plane of incidence and is called p-polarized or transverse magnetic (TM).
It is depicted by a short double arrow.
8
2. Theory
One of the beams obeys Snell’s law of refraction and is known as the ordinary ray, the second
beam, which does not obey Snell’s law, is known as the extraordinary ray. They propagate at
different phase velocities and can be characterized by different refractive indices.
Figure 2.5 Separation of ordinary and extraordinary rays in passing through a sheet of calcite [11].
When the calcite sheet is rotated about the incident ray the deviated ray rotates at the same
rate. An observer sees two images when looking through the crystal. The ordinary, undeviated
ray forms an image by light with its electric field vector in the plane perpendicular to the optical
axis. The electric field vector of extraordinary, deviated ray is then perpendicular to the ordinary
ray.
Birefringent materials are used to modify the SOP, like turning a linear polarization into a
circular one or physically separate a beam into two orthogonally polarized components. The
former can be achieved with a retarder or a wave plate whereas the latter is realized with
different types of polarizing cubes. The terminology of the axis of a crystal may be confusing,
but is defined by the refractive indices. If the refractive index of the extraordinary beam ne is
smaller than the refractive index of the ordinary beam no, then the extraordinary axis is fast and
the ordinary slow. Conversely, if ne > no, as for calcite for instance, then the extraordinary axis
is slow and the ordinary fast.
Wave plates can be fabricated either from a single piece of birefringent crystal or from a
combination of two pieces of crystal. They change the phase difference between two
orthogonally polarized components by a specific amount, but not the electric field vector itself.
Depending on the desired function, different wave plates are commercially available. The
quarter wave plate (QWP) introduces a phase shift of 𝜋⁄2 and thus converts a linear polarized
beam into a circular polarized one as can be taken from Figure 2.2.
Retarders are offered in three different types. The cheapest version is the multi-order wave
plate. They can be easily fabricated, but are very sensitive to wavelength, incident angle,
9
2. Theory
temperature and have a narrow field-of-view. By combining two multi-order wave plates in a
way that yields the desired phase difference, one creates a zero-order wave plate. Temperature
variations can be compensated by aligning the fast axis of one wave plate with the slow axis of
the other. Layering multiple of these wave plates perpendicular to the optical axis further
improves retardation stability to wavelength shifts [12]. The highest stability over a broader
wavelength range is offered by the achromatic wave plates, which also are the most expensive.
They are created by aligning the fast axis of a multi-order wave plate with respect to the slow
axis of a magnesium fluoride or UV sapphire wave plate [13].
Another convenient method of modifying the retardance is with liquid crystals (LC). Its
molecular orientation can be easily altered by low-amplitude electric or magnetic fields and by
small changes in temperature or mechanical pressures. LCs are classified into four different
types: cholestric, smectic, discotic and nematic. Their main difference is the shape and
orientation of the molecules as visualized in Figure 2.6. The nematic LC is further distinguished
between its molecular orientations within the container or the influence by the surface of the
inner walls of the cell. The three types are homogeneous, homeotropic and twisted with their
crystals parallel to the cell wall, perpendicular to it or the molecules are parallel like in the
homogeneous version, but twisted by 180° between the walls, respectively.
Figure 2.6 Types of liquid crystals. (a) Cholestric crystal; (b) Smectic liquid crystal; (c) Nematic liquid
crystal; (d) Discotic liquid crystal in nematic-like orientation [14].
One field of application of the twisted nematic liquid crystal is to use it as a tuneable wave plate
or retarder. A nematic liquid crystal displays a birefringence like a uniaxial solid crystal, as the
previous mentioned calcite. The molecular axis of the nematic LC can be rotated by applying a
rotating external electric field in the form of a sinusoidal voltage, thus realizing a rotatable wave
plate [14].
10
3. Setup
3. Setup
3.1 Idealized schematic
The first schematic can be seen in Figure 3.1. It already features the principle of a confocal
microscope. Starting from the left, random polarized light Polx,random is collimated by the
objective to form a free beam. This beam gets linear polarized Polx,linear by the first polarizer P,
reflected at the non-polarizing 50/50 beam splitter (BS) and focused on the sample with a highNA objective. Its reflection from the sample passes the beam splitter, whereas the reflection on
the beam splitter is neglected, and suppressed by the second linear polarizer A (which stands
for analyzer), which is set perpendicular to the electric filed vector of Polx,linear. The emitted
beam from the sample is of the same wavelength, but of different polarization Pols,different than
the excitation beam. Therefore, it will experience only a fraction of the suppression of the
excitation beam and thus can be detected.
SM Fiber
A
Linear polarizer
+ rotator
SM Fiber
PolX
PolX
random
linear
P
objective
Linear polarizer
+ rotator
Pol. axis
(Analyzer) ┴
PolX,lin
50/50
Non polarizing
beam splitter
Eo
PolX
linear
PolX
linear
PolS ≠ PolX
PolS
NA=0.95
different
Sample
Figure 3.1 Idealized schematic.
The next step is to integrate further components (Figure 3.2) with the main goal of
achieving the desired extinction ratio of at least 1×106. The polarization control paddle
(Thorlabs FPC560) is necessary to optimize the intensity by adjusting the state of polarization
(SOP) of the light coming from the fiber dependent on the angle of the first linear polarizer.
11
3. Setup
After the reflection at the BS, a quarter-wave plate (QWP) is responsible for changing the SOP
at the sample to circular polarization. This is often desired to perform experiments based on
electronic or magnetic spins induced in the sample. The reflection of the excitation beam passes
the QWP a second time and gets linear polarized again, but now rotated by 90°. The tunable
retarder is recommended for compensation of any polarization changes induced by the optical
components. Any surface may alter the linear polarization of the free beam and lead to small
ellipticities, which cannot be perfectly blocked by the analyzer anymore and obscure the
detection of the sample emission. So, both parts only serve a functional purpose.
Detection
Arm
SM Fiber
Linear polarizer
+ rotator
Tunable retarder
Excitation Arm
Linear polarizer
+ rotator
SM Fiber
Pol. paddle
50/50
Non polarizing
beam splitter
Eo
objective
λ/4 + AR
coating + tilt
Sample
Arm
Sample
Figure 3.2 Idealized schmetaic including functional components (QWP, tunable retarder).
The design is divided into three “arms” or blocks:

The detection arm consists of the optional tunable retarder, the analyzer, fiber
focusing unit and detector.

The excitation arm contains the laser source, manual fiber polarization controller,
fiber collimation unit and linear polarizer.

The sample arm includes the optional QWP, focusing high-NA objective and
sample, which is realised by a simple mirror in this case.
The non-polarizing beam splitter represents the combining unit for all three arms.
12
3. Setup
3.2 Integration capability into attoCFM I
The second step is to guarantee the implementation of all used or required components into
the new developed attoCFM I head. Before going into detail about the integration, it is
important to understand the functionality of the attoCFM I and its design from Figure 3.3.
2
1
5
CFM head, top parts
6
3
4
8
7
1: Detection coupling unit
5: Excitation coupling unit
2,3,4,6,7,11,12:
Silver protected mirror
8: Beamsplitter 50:50
10: CCD and LED block
13: Vacuum window
1
0
CFM head, lowest stage
+ vacuum throughput
1
2
1
1
1
3
xyz-stage + sample
Figure 3.3 attoCFM I design.
This is a multi-stage device with independent units that are built on top of each other and
guide the beam at one specific corner using a beam splitter for each level. The top and middle
stage are virtually the same units, whereas the top section is used as the detection and lower
part as the excitation channel. In general, both designs are possible, with the detection channel
arranged in front of or after the excitation channel. The lowest level consists of the inspection
optics, including an LED to illuminate the sample and facilitate coarse positioning of the
sample. The CFM head connects with a vacuum window, consisting of a 7° tilted window inside
of a cage plate to avoid etalon effects, to the cryogenic station. The free beam propagates inside
the cryostat until it hits the sample that is placed on top of a coarse positioning xyz-stack plus
optional scanning positioners for fine adjustment.
13
3. Setup
When developing the breadboard setup, emphasis is put on a copy of the existing design
as much as possible to reduce the amount of unknown parameters. Every identical component
reduces the risk of unknown behaviour after the implementation into the actual CFM head. This
is the reason why additional mirrors are introduced in the breadboard copy drawn in Figure 3.4.
However, the inspection optics are excluded, because they are only used once for the alignment
and do not have a significant influence on the system. One can see the similarities in
components compared to the attoCFM I design from Figure 3.3 in Figure 3.6 from the following
chapter. Additionally, the excitation, detection and sample arm are indicated to see the
connection to the previous discussed schematic from Figure 3.2.
1: Detection coupling unit
5: Excitation coupling unit
2,3,4,6,7,11,12:
Silver protected mirror
8: Beamsplitter
13: Vacuum window
1
2
4
3
7
8
13
12
5
11
6
sample
Figure 3.4 Breadboard copy of the CFM head.
3.3 Final setup
3.3.1 Setup design
Now as the principle design was discussed, the next step is to form a compatible breadboard
setup following the guidelines from the previous chapter 3.2. The first drawing in Figure 3.5
demonstrates the general design and position of fixed components like mirrors (indicated by a
capital M) and the excitation (X) and detection (D) unit.
14
3. Setup
Md3
Mx1
Md2
BS
Mx2
Ms1
D
X
Md1
vaccuum
window
Ms3
Ms2
Figure 3.5 First general design following attoCFM I integration guidelines.
The mirror Ms3 acts as the sample holder having an objective (Olympus MPlanApoNx50) with
an extraordinary high NA of 0.95 positioned in front of it. The excitation ray path is indicated
by the red solid line, the reflection path by a green line. In order to keep the sketches first simple
and comprehensible, Figure 3.6 further includes the first linear polarizer P1 (Thorlabs
LPVIS050), the second linear analyzer P2 (same model as P1), the position of the tunable
retarder (Meadowlark LRC-100-IR1), the optional inspection optics that were used once for the
alignment process and highlighted areas for the designated arms.
Detection Arm
Excitation Arm
Md3
Mx1
Md2
Mx2
analyzer
P2
polarizer
P1
tunable
retarder
BS
Ms1
Md1
BS
CCD
f = 100
vaccuum
window +
QWP
NA = 0.95
Inspection Optics
optional
Ms3
Ms2
Sample Arm
Figure 3.6 Complete setup with highlighted blocks/arms and optional Inspection optics.
A high value is set on the general design of the setup with the goal to keep it as compact as
possible. The ray path is kept at a height of approximately 5 cm to reduce the impact of
vibrations. The full space of the breadboard is 45 x 30 cm and comparably small considering
15
3. Setup
the amount of components. It is troublesome finding a possible spot for every part by randomly
QWP
positioning and shifting the components around, thus a template is built in Microsoft
PowerPoint with all required dimensions of the components and the breadboard. This highly
improves and accelerates the process of finding a proper configuration that is customizable at
the same time. The result is shown in Figure 3.7 where the ray path is indicated by the red line.
All components are measured and created with Microsoft PowerPoint using their actual
dimensions, including the breadboard and the hole pattern.
LASER
LCVR
Detector
P1
P2
Figure 3.7 Finding the best design with a PowerPoint template.
The exact realization is demonstrated in Figure 3.8 from the top view. The red line indicates
the excitation ray path, the green line follows the detection ray path. The QWP is mounted right
in front of the sample mirror. No further components are set up.
16
3. Setup
Figure 3.8 Top view of one setup. Red line indicates the excitation, green line the detection ray path.
3.3.2
Choice of components
All components are optimized for the near infrared (NIR) wavelength region around 900 nm,
which is the desired wavelength for quantum dot measurements. Since the attoCFM I head is
fiber coupled, both excitation source and detection path need to be implemented accordingly.
Both units are copied from the attoCFM I. A plan objective (Olympus PLN10x) is mounted on
a z-stage in front of a fiber adapter plate (SM1FCA). The linear stage in the attoCFM I is a
special design to fit the dimensions and housing, which cannot be used on the breadboard setup.
Here, two commercial products are used. The Thorlabs CT1 model for the excitation and sample
arm and the Thorlabs SM1Z model for the detection arm. The main difference between these
translators is the longer stage travel of the CT1 of 13 mm with its ball bearings compared to the
flexure bearing of the SM1Z, providing 1.5 mm maximum travel range. Both stages show
difficulties in operation when trying to couple the laser light that will be addressed further. All
silver mirrors (Thorlabs PF10-03-P01) offer high reflection in the visible-NIR spectrum and
are coated with a SiO2 layer to protect them from oxidation.
The choice of a polarizer highly depends on its application. Many different types and forms
are commercially available at a vast price range. One has to choose between factors like
temperature influence, laser damage threshold, angle tolerance, transmission, beam deviation
or aperture size [15]. The polarizers for this project are used because of the high extinction ratio
of more than 1×108 in the wavelength region of 900 nm, according to the data sheet in Figure
17
3. Setup
3.9. This is achieved by a thin film of ellipsoid nano particles embedded in Sodium-Silicate on
a crown glass (B270) substrate [16]. The transmission is indicated with 81%. An acceptance
angle of ± 20° facilitates positioning the polarizers and reduces potential risk of misalignment.
In order to keep the costs low the ½ inch version is chosen.
Both polarizers are placed in a high precision rotation mount (Thorlabs PRM1/M). It offers the
highest rotation precision for a moderate price. When locked, the micrometer drive provides
2.4 arcmin resolution between the divisions. One potential complication that leads to
malfunction when working with polarizers is stress induced in the material. In order to reduce
this risk, both polarizers are fixed with stress-free retaining rings (Thorlabs SM05LTRR).
Figure 3.9 LPVIS Series Transmission and Extinction Ratio
The beam splitter consists of an UV fused silica plate at a 70:30 ratio. Figure 3.10 shows
the most linear behaviour for s- and p-polarized light for the 70:30 version, which can be of
advantage when changing the source wavelength. A thickness of 5 mm should not lead to ghost
images created by reflections on the inner surfaces. Additionally, an AR coating for 700 – 1100
nm is applied.
Figure 3.10 Beam splitter BSS11 transmission.
The tunable retarder is realized by a liquid crystal variable retarder (LCVR) from
Meadowlark Optics (LRC-100-IR1) based on the twisted nematic structure. The outer diameter
18
3. Setup
of 1 inch fits the dimensions of the setup and is crucial for a further possible implementation
into the attoCFM I head. A solid line indicates the fast axis on the LCVR housing. In order to
maintain repeatable measurements the LCVR is mounted in a rotation cage plate and fixed with
a screw (Figure 3.11). The Basic Liquid Crystal Controller (Meadowlark D4010) is used to
operate the LCVR with a square drive waveform at 2 kHz. The user has the option of applying
two different voltages in the range of 0 to 20 V that can be modulated or manually switched.
Besides, an external modulation source can be connected. However, in this case no modulation
is required and the LCVR is only controlled by changing the voltage. Conventional LCVR
operate at a retardance range of 30 nm to λ/2. In order to achieve smaller retardation the LCVR
is attached with a compensator that achieves the full range of 0 to λ/2.
Figure 3.11 Liquid crystal variable retarder (LCVR) in rotation cage plate.
The QWP is used to create a circular polarization at the sample. In order to get a perfectly
circular polarization an accordingly well-designed QWP is mandatory. These either require
custom designs to match the desired wavelength or can be realized with expensive achromatic
wave plates, However, the general idea and usage can still be tested with a zero-order QWP
that has the best cost-performance ratio. Figure 3.12 shows the performance of the WPQ05M980 zero-order quarter wave plate indicated in red, compared to the achromatic wave plate in
purple. For this purpose, the zero-order version is close enough to 0.25 wave retardance and
sufficient for the task. The QWP is tested within two different mounts. First, it is positioned in
a manual cage rotation mount (Thorlabs CRM1/M) and afterwards glued on a piezo actuated
rotation mount (attocube ANR-204). The results will be discussed in chapter 4.1.1.
19
3. Setup
Figure 3.12 Wave plate performance.
3.4 Alignment procedure
The alignment is very laborious and can lead to severe issues when not monitored from the
very beginning. Generally, it is important to check whether the beam is still in the middle of the
optical axis after every component. The alignment of the final setup is divided into several
steps, which will be explained and supported by sketches in order to provide a full, step-by-step
guide.
3.4.1 Collimation of beam
The first step is to produce a collimated beam after the fiber coupling unit. This block consists
of a fiber, fiber coupler, objective, z-translation stage, two mirrors in kinematic mounts and a
Laser-Detector Module (LDM600), a fiber coupled module, which provides both a laser light
at 635 nm and a detector. Before fully assembling this block it is advisable to roughly adjust
the distance and tilt of the objective on the translation stage (depending on the translation stage
model). It turned out, that the model CT-1 from Thorlabs doesn’t offer a guaranteed
perpendicular and centric orientation of the objective in respect to the optical axis. First,
assemble the z-stage and the fiber coupler, add long extension rods (> 20 cm) and add a cage
plate at the end with an alignment disk. Move the objective inside its’ loosened mount until a
centric beam is achieved and fix the position. Remove the alignment disk and project the beam
on any white surface in the room, which is at least two or three meters away. Move the z-stage
to create a collimated beam by checking the beam diameter at different positions until it is
roughly the same at all points on the axis. Consider the working distance from the objective as
a starting point for positioning it in front of the fiber adapter. Add the first mirror (M1) in 45°
orientation to the beam path and the second mirror (M2) perpendicular to beam propagation,
which now creates a first confocal configuration as expressed in Figure 3.13.
20
3. Setup
Figure 3.13 Confocal setup for objective adjustment and mirror alignment for excitation and detection
arm.
The LDM600 is internally equipped with a 50/50 coupler that allows for measurement of the
reflected beam from the same channel (fiber). The following step ensures the best possible
coupling of the laser.
Adjust tilt angles θ for pitch and φ for the yaw angle, respectively from the mirrors. Iteratively
maximize the signal by tilting the mirrors and moving the objective along the z-axis. When a
high signal peak is being observed one has to check, whether the beam is collimated or focused
on M2 as two scenarios can apply for a signal peak that are described in Figure 3.14. If the
objective is not exactly at its working distance but at a point f’ > f, it is possible for the beam
to be focused on the mirror M2 and be coupled into the fiber. This can be checked by moving
the objective with the z-stage and observing the signal. If there are two distinct signal peaks,
the peak closer to the fiber adapter corresponds to the collimated beam. The longer the beam
path, the shorter is the difference between f and f’. In this setup the difference is smaller than
750 µm. This procedure has to be done for both detection and excitation arm.
Figure 3.14 Development of two focused points at positions f and f' > f.
After collimating the beam, further mirrors and parts can be added successively.
In order to achieve paraxial beam propagation it is recommended to work with two pinholes,
like two diaphragms or alternatively a diaphragm and an alignment disk. After adding a mirror
to the setup, extension rods are placed after the mirror of at least 5 cm in length to position the
pinhole. The first diaphragm is placed close to the mirror, the second as far away as possible.
Figure 3.15 shows the principle, with the paraxial (solid line) and a misaligned (dashed line)
21
3. Setup
beam. Tilting mirror M2 will lead to small changes of the spot on the diaphragm, but a bigger
displacement on the alignment disk, which is further away. Now, M1 is used to centre the spot
on the diaphragm and M2 to centre the spot on the alignment disk. These steps, also called
“beam walking”, have to be repeated until the beam is centred and parallel to the optical axis.
After this, the next part can be added and the procedure repeated.
Figure 3.15 Principle of beam walking using two mirrors M1, M2, one iris diaphragm and an alignment
disk.
This method has to be done for both excitation and detection arm separately, which are
highlighted in Figure 3.16. When aligning the detection arm (green beam) all mirrors Ms1, Ms2
and Ms3 from the sample arm mustn’t be used anymore, since otherwise the excitation arm will
get misaligned again.
Figure 3.16 Setup with fixed components and optional inspection optics.
22
3. Setup
As soon as the detection and excitation arm are aligned, both arms are coupled to a laser
source and the inspection optics, consisting of a beam splitter (Thorlabs EBS1), focusing lens
(f = 100) and CCD camera, is introduced. The lens is focused to infinity to image the reflection
of the sample mirror Ms3 from both sources, which need to overlap on the CCD camera using
only mirror Md2. After successfully overlapping the spots, the inspection optics can be removed
again. The laser source from the detection block is then replaced with a detector (FEMTO OE200-IN1), the signal maximized with a combination of tilt from mirror Md2 and very small
movement on the z-stage of the detection and excitation block.
The focused spot radius, w0, is calculated from the focal length, f, and beam diameter, w
f
(1.12)
w
The f-number, f#, is defined as the quotient between the focal length f and diameter of the
entrance pupil, limiting the beam diameter to 2w and is given for the used objective [6]. The
spot diameter is calculated with f# = 22 to w0 = 12.6 µm, thus overexposing the core of a singlemode fiber with a diameter of 5 µm.
w0 
3.4.2
Laser coupling
Coupling of the laser source is done in a separate step. The direct laser output is specified with
5 mW power at 905 nm, thus falling in the category of a class 3R laser type. In order to avoid
accidents in the laboratory, like a reflected beam hitting the naked eye, the whole laser coupling
unit is put into a box (Figure 3.17) and finally covered with a black fabric. Only the output
fiber, detector power and signal cable are put through the handle slots of the box.
Figure 3.17 Laser coupling unit inside box.
23
3. Setup
The laser (TOPAG TECIRL-7G-905) is fixed on a V-clamp holder. The beam splitter is of
an unknown model, but an experiment leads to a 70:30 relation. The same objective (Olympus
PLN10x) is used as in the excitation and detection block, mounted on a z-stage (Thorlabs
SM1Z). The detector (PDA36A-EC) will be used to measure the coupling of the excitation
block for this wavelength.
Mx2
z-stage
z-stage
M02
fiber
objective
objective
M1
Detector
Mx1
f = 50
M01
Excitation Block
Figure 3.18 Schematic of the laser source and additional excitation arm for the alignment process.
First, the laser is coupled into the fiber as described in chapter 3.4.1 using the “beam walk”
method and monitored on a detector (FEMTO OE-200-IN1) to achieve the highest possible
output power from the unit. Afterwards the fiber is detached from the detector and connected
to the excitation block. An extra mirror M1 is put after Mx1, in order to avoid misaligning the
setup, and now creates a new confocal configuration. Tilt M1 until the signal is back reflected
into the laser coupling unit; adjust the z-position of the objective from the excitation block and
M1 to gain a high signal on the detector. Background noise has to be considered when aligning
the setup, caused by reflections within the box. Note, that tilting mirror M01 or M02 may lead
to a higher signal, but reduce coupling efficiency and therefore mislead the user.
3.5 Working procedure: Gain maximum Extinction Ratio
This working procedure explains all necessary steps to get the highest extinction ratio in
case of the following, fully aligned setup in Figure 3.19. Excitation and detection arm are
comprised in the corresponding boxes (X) and (D).
24
3. Setup
high-NA
M1
BS
TS2
P1
P2
TS1
Figure 3.19 First simplified setup schematic including both polarizers P1, P2 and the high-NA objective.
Excitation and detection arm are comprised in X and D.
The first polarizer P1 has to be set with its transmission axis in vertical or horizontal
position (note: procedure to determine the transmission axis from a polarizer is explained in the
following chapter Figure 3.6). Analyzer P2 needs to be parallel to the polarizer in order to get
the maximum throughput. Moving the polarization control paddles may increase the signal
depending on the SOP of the laser. This voltage will be used as Umax. Rotate P2 by 90°,
independent of the direction. Now, both rotators are locked for fine adjustment usage, P1 rotated
by a small angle, so that an increase in signal can be observed and afterwards the new minimum
found by rotating P2. Assuming the position of the polarizers is close to the highest ER, an
optimization development should yield a decline pattern as sketched in Figure 3.20. If small
rotations of P1 don’t have a significant influence on Umin, bigger rotation movement should be
applied and again the new voltage minimum found by adjusting P2. In general, the bigger the
achievable extinction, the more sensitive is the polarization rotation. This is determined by the
the Malus’ law and further discussed in chapter 2.2.3.
U
t
Figure 3.20 Pattern for optimizing extinction ratio ER.
25
3. Setup
3.6 Determination of polarization axis
The orientation of polarization plays a major role in achieving highest extinction ratios, as
will be shown in chapter 4.1. One common way to determine the polarization plane of an
unknown component is by adding a polarizing device with a known polarization plane and
monitor the outcome. Figure 3.21 shows the setup with the laser source (attocube LDM600, λ
= 635 nm), a non-polarizing beam splitter bs1 (Thorlabs BSS11) – can also be replaced by a
mirror – the polarizing beam splitter bs2 (Edmund Optics EO G47-125) with a design
wavelength of 632.8 nm and extinction ratio between p-polarization transmission Tp and spolarization transmission Ts of Tp/Ts >1000:1 at its design wavelength. An InGaAs detector
(Thorlabs PDA10CS-EC) is used to monitor the power.
polarizer
bs1
detector
bs2
source
Figure 3.21 Configuration to determine the polarization axis.
The intensity reaches its maximum when the polarizer and beam splitter are at the same
polarization plane. When Ts is suppressed the result is a horizontally polarized wave. On the
contrary, the intensity is at a minimum for a vertically polarized wave when the polarizer is
rotated by 90°. The results are summarized in Table 3.1, with the angle noted from the rotation
mount. The shape of the intensity is sharper at the minimum than at the maximum and thus can
be determined with a better accuracy.
Table 3.1 Polarization axis of polarizers P1 and P2. Angles are read from each rotation stage.
Polarization Angle [ °] Angle [ °]
rotation
Polarizer P1
Polarizer P2
Horizontal
175
355
Vertical
84.4
264.4
Horizontal
115
295
Vertical
25.3
205.3
26
3. Setup
3.7 Transmission
3.7.1
Coupling efficiency for collimated beam
The coupling efficiency of the excitation and detection arm is of interest to ensure proper
installation of the system. The attoCFM I alignment is usually calibrated with the LDM600, a
laser detection module consisting of an internal 50/50 coupler that directs the back reflections
from a mirror in the sample arm to a detector. This provides a convenient method for optimizing
the collimation at the excitation arm and the focusing of laser light into the fiber at the detection
arm. However, the system in this project is designed for operation at 905 nm and requires
another setup but uses the same method, which is explained below.
First, one needs to calibrate the photodiode in order to get a reference voltage for a known
reflection. Then it is possible to calculate the actual efficiency of the system including the
objective and fiber. This works identical for both excitation and detection arm. A known
reflection of 4% occurs at the end of a FC/PC fiber. The fiber is cut perpendicular so that back
reflections are coupled back into the fiber, in contrast to the FC/APC connector with a wedged
ending to prevent such back reflection. The reference voltage Uref (Figure 3.22 (a)) is derived
from the measured voltage with the FC/PC cable UFC/PC, reflectivity rFC/PC of 4% and the
voltage offset from the laser source Uoffset
U ref 
U FC / PC  U offset
rFC / PC
(1.13)
Afterwards, the fiber can be connected with the excitation or detection arm (Figure 3.22 (b)),
the signal optimized as described in Chapter 3.4.1, the current voltage, Ux, measured and the
reflectivity, Rx, described as
Rx 
U x  U offset
U ref
(1.14)
Changing the connection of the laser source from the FC/PC fiber patch cable to the FC/APC
cable may lead to misalignment of the laser coupling and distort the signal. Therefore, the 4%
reflection of the used FC/PC cable has to be considered when measuring the new voltage Ux,PC
by
U x, PC  U FC / PC  U x '  U x '  rFC / PC 
(1.15)
with the actual voltage, Ux’
U x' 
U x , PC  U FC / PC
1  rFC / PC
(1.16)
Ux is then replaced with Ux’ in equation (1.14). Finally, since the system is passed wice by the
laser the coupling efficiency µ is calculated by
  Rx
27
(1.17)
3. Setup
(a)
Laser source
FC/PC
Exc/Det arm
(b)
Laser source
Figure 3.22 Setup for measuring the coupling efficiency of the excitation and detection arm. (a)
Measurement of U(FC/PC); (b) measurement of U(x,PC)
3.7.2 Other transmission results
All remaining transmission measurements were performed with the free beam by measuring
the intensity before and after each component. The whole setup is characterized with the basic
parts, consisting of the polarizers being parallel to each other in s- or p-polarization, all mirrors
and the beam splitter. The transmission Tsetup is calculated from
TSetup  ExcitationArm  DetectionArm   rmirror   t BS  rBS
n
(1.18)
with the coupling efficiency of the excitation arm, µExcitationArm, and detection arm, µDetectionArm,
reflectivity of a mirror, rMirror = 0.98, the amount of mirrors, n = 10, transmission and
reflectivity of the beam splitter, tBS = 0.7 and rBS = 0.3. All results are summarized in following
Table 3.2. All transmission results agree with their expected value.
Table 3.2 Summary of transmission results.
Part or setup
Value
Coupling efficiency ηExc/Det (SM fiber objective PLN 10x, 905nm)
Transmission of Objective Olympus PLN 10x, NA = 0.25 (collimator)
Maximum transmission of linearly polarized light (Pol || Axis of polarizer)
65% ± 10%
77%
85% ± 2%
Transmission of objective Olympus MPlanApoN50x,
NA = 0.95 (sample objective)
49%
Transmission of Liquid Crystal Variable Retarder (LCVR)
98%
Transmission of quarter wave plate (QWP)
91%
Whole Setup with P1 and P2 (P1||P2, if P1 transmits S or P-polarisation)
28
5%
(calculated: 6.7%)
3. Setup
3.8 Angular resolution of polarizer
When operating at the limit of the possible extinction capability of the polarizers, it is
crucial to know whether the system is capable of achieving the desired polarization. A
mathematical simulation of the required angular resolution is based on the Malus’ law given in
chapter 2.2 by the equation (1.10). A visual interpretation is given in Figure 3.23. Plot (a) shows
the function f(θ) = cos²(θ) with θ between -180° and +180°, and with a logarithmic y-axis in
plot (b). The zoomed in graph (c) demonstrates the sensitivity of the angle θ that is necessary
to achieve the desired extinction plotted on the y-axis.
(a)
(b)
(c)
Figure 3.23 Mathematical angular resolution requirement. (a) f(θ) = cos²(θ), linear scale; (b) f(θ) = cos²(θ),
logarithmic y-axis; (c) f(θ) = cos²(θ); logarithmic y-axis, zoomed in.
Table 3.3 summarizes the calculated required angular resolution for extinction ratios from
1×106 to 1×108.
29
3. Setup
Table 3.3 Required angular resolution for the according extinction.
Extinction Calculated required
Ratio
angular resolution [deg]
1×106
± 0.06
1×107
± 0.02
1×108
± 0.006
The angular resolution of the rotation mount is 0.04°. However, using the fine adjustment screw
of the rotation mount smaller changes can be achieved in between each tic. This ensures that
theoretically an extinction ratio of > 1 × 106 is possible with these components.
3.9 Influence of beam splitter
Using just one polarizer before the beam splitter (Thorlabs BSS11) in the setup it is possible
to determine a change in transmission intensity, depending on the orientation of the polarization
set by the polarizer. In order to attain the maximum intensity, P1 needs to be parallel to the SOP
of the laser source. Therefore, after rotating P1 by 10° steps the signal is maximized by adjusting
the polarization control paddles, ensuring optimum transmission. The detector voltage is plotted
against the angle of excitation polarizer P1 in Figure 3.24. One can see a sinusoidal evolution
of the detection voltage, creating two maxima and minima at 90° difference between each other.
In this configuration, the beam splitter is always passed twice. First, the excitation beam is
reflected at the beam splitter surface and afterwards the reflection passes through the beam
splitter again to the detection arm.
Umax
Umin
Figure 3.24 Influence of beam splitter on throughput.
30
3. Setup
Taking the optical properties of the beam splitter into account one can describe and quantify
this behaviour. Figure 3.25 provides (a) transmission and (b) reflectance values for p-, s- and
unpolarized light at 45° angle of incidence (AOI).
(a)
(b)
Figure 3.25 Optical properties of the beam splitter BSS11. (a) Transmission; (b) Reflectance.
The complete throughput of the beam splitter is determined by the product of the
transmission and reflectance at 905 nm for the according state of polarization. Two situations
are evaluated for p- and s-polarized light

Throughput p-polarization: THP = TP ∙ RP = 0.19 ∙ 0.85 = 0.162

Throughput s-polarization: THS = TS ∙ RS = 0.45 ∙ 0.56 = 0.252
Now, the expected relation between minimum and maximum intensity is given by the ratio
THP / THS = 0.64. This agrees with the relationship between Umin / Umax = 1.89 / 3.2 = 0.59 of
the experiment. Consequently, one can see how important the state of polarization in terms of
system throughput is and depending on the user’s demands, the type of beam splitter needs to
be thoroughly evaluated.
31
4. Results
4. Results
4.1 Extinction Ratio
The main task of this project is to achieve an ER of at least 1×106. The first ER
measurement setup consists of a simple, straightforward alignment with as few parts as
possible, even without the beam splitter (Figure 4.1). The method of adding parts successively
allows for detailed analysis of the implemented components.
P1
P2
Figure 4.1 First setup to determine ER without the beam splitter.
This configuration yields the very first extinction ratio measurement with values ranging
from 7.5×104 to 2×105. Taking the data sheet of the polarizer into account, it is not clear why
the extinction is three orders of magnitude below the specification. Thorlabs does not provide
a clear explanation of the fulfilment of the specification. Even though these results hardly fulfill
the requirement of an ER at least 1×106, further components are added to build the complete
setup as described in chapter 3.3.
A new simplified schematic is introduced here to visualize the configuration for the performed
measurement. The excitation and detection arm were already symbolized with the X and D box
in chapter 3.5 and the previous Figure 4.1. The following simplification integrates the alignment
mirrors into the X and D box to provide a clear schematic, highlighting main components. A
summary of three different configurations and the range of feasible ERs is provided in Figure
4.2. In section (c) the thin film beam splitter is replaced by a cubic beam splitter (Thorlabs
BS020), which has a smaller difference in transmission between s- and p-polarization. Within
each configuration, the reproducibility varies within one order of magnitude or more and it is
not clear which configuration consistently provides the highest ER. Any small change in mirror
tilt, material contraction or expansion or vibration leads to a decrease in ER in this highly
sensitive configuration. However, even considering the inconsistent reproducibility of ER the
requirement for a signal suppression of at least 1×106 is given here in all cases.
Interestingly, one can see that a higher extinction is possible with the introduction of the
beam splitter. This effect is not further examined, but it seems that the beam splitter has a
positive effect on the linearity of the polarization, since higher extinction is possible.
32
4. Results
P2
5×106 – 8×107
(a)
P1
NA=0.95
P2
5×106 – 5×107
(b)
P1
P2
NA=0.95
(c)
BS020
3.5×106 – 1×107
P1
Figure 4.2 Summary of different configurations and according range of extinction ratios on the right. (a)
Polarizer P1 and analyzer P2; (b) both polarizers P1, P2 and sample objective; (c) both polarizers P1, P2,
sample objective and different beam splitter.
A general dependency on the angle of the polarizer P2 can be observed in Figure 4.3. The
angle of the polarizer P2 (please be aware that usually P1 is used as the polarizer) is rotated and
the suppression is optimized using the analyzer P1. After each change in rotation angle of P2
the signal is optimized with the polarization control paddles first. Each of the four peaks
corresponds to either s- or p-polarization axis of the excitation polarizer P2. Consequently, one
can only achieve highest extinction with the SOP of the excitation beam close to its vertical or
horizontal polarization. The rotation angle is not exactly the same for every experiment, but
needs to be slightly adjusted every time something in the setup was added or changed,
deliberately or not. For instance, it is possible to tilt one mirror (range of µrad) to slightly
misalign the focused beam (range of tens or hundreds of nm) in the detection arm, but achieve
high extinction again after adjusting the rotation angle of polarizer and analyzer.
33
4. Results
1E+08
horizontal
polarization
1E+07
Extinction Ratio
1E+06
1E+05
1E+04
1E+03
1E+02
1E+01
vertical
polarization
1E+00
0
50
100
150
200
250
300
350
400
Angle of polarizer [deg]
Figure 4.3 Extinction ratio as a function of the polarizer angle.
4.1.1 Influence of QWP and LCVR
Chapter 3.1 discussed the design including the QWP at the sample arm and the option of
improving the ER with a tunable retarder. First, the QWP is glued on a rotation cage plate and
placed in the sample arm (Figure 4.4 (a)) and the fast axis set parallel to the polarization of the
incident light. In this position the QWP doesn’t affect the SOP and thus virtually not altering
the extinction. The usual operation of the QWP would be at 45° of its fast axis relative to the
SOP of the incident light to create a circular polarization at the sample. After the second pass
of the reflection the SOP is turned again, yielding linear polarization in perpendicular direction
of the incident SOP. Therefore, the analyzer P2 needs to be rotated by 90°, with respect to the
previous test, to achieve suppression. In this case the ER drops by at least one order of
magnitude, because it is not possible to create a perfect circular or linear polarization with the
QWP. One solution is the usage of the attocube ANR240 rotator, which offers a 12.7 mm wide
aperture for transmission experiments. The high precision of this rotator allows for extinction
ratios with the QWP at 45° at the expected range from Figure 4.2.
P2
QWP
QWP
P1
LCVR
P2
P1
(a)
(b)
Figure 4.4 Simplified setup to determine influence of (a) QWP and (b) ER increase with LCVR.
34
4. Results
Another suggestion is to eliminate small ellipticities by the implementation of a tunable
retarder or here, the liquid crystal variable retarder (LCVR) from Meadowlark Optics (LRC100-IR1). The position right before the analyzer is supposed to additionally compensate for
disturbances caused by the beam splitter and create a perfect linear polarization. However, no
increase in ER is achieved.
Now, since both components are tested and particularly the LCVR achieved no
improvement, the QWP and LCVR are left out of all further studies to reduce nonessential
parameters as discussed in chapter 3.1.
4.1.2
Influence of vacuum window
Another part that has to be considered is the vacuum window that connects the whole attoCFM
I head with the cryostat. It consists of an uncoated BK7 glass placed at a 7° angle into a custom
designed cage plate. The experiment has the following setup from Figure 4.5, consisting of both
polarizers and the sample objective. In total, there are four possible mounting positions of the
vacuum window, since no explicit rotation requirement is given for the final assembly.
vacuum
window
NA=0.95
P2
P1
Figure 4.5 Setup to determine the influence of the vacuum window.
No significant change in ER is observed for all window positions, including the absence of
the window (position 0), which can be taken from Figure 4.6. However, it is noteworthy that
the angle of polarizer and analyzer for high extinction differs at positions 1 and 3 compared to
positions 2 and 4 by 10°.
35
4. Results
Extinction Ratio
1E+08
1E+07
1E+06
1E+05
0
1
2
3
4
5
Window position
Figure 4.6 Extinction ratio at different vacuum window positions.
One can see in Figure 4.7 that ⃑E is parallel to the incident plane of the window at positions
2 and 4 and perpendicular at positions 1 and 3. The propagation direction is indicated with the
vector ⃑k, the window by a blue solid line at small angle. One can imagine the schematic as a
side view of the setup. This information can be useful for troubleshooting, when the customer
changes the orientation of the attoCFM I head, leaves the polarizers at the same position and
suffers performance loss.
1
2
E
3
k
E
k
Window inside
cage plate
4
E
k
E
k
Figure 4.7 Vacuum window positions according to the orienation of the E-vector to the window.
4.1.3 Spatial filter
The confocal microscope eliminates out-of-focus information with a pinhole, which is replaced
with the aperture of the fibre in our case. Additionally, mode propagation in the fiber itself is
analyzed. The importance of the usage of a SM-fiber is shown here. Tests are conducted at two
different wavelengths, 905 nm and 635 nm, at different modes inside the fiber and finally
replacing the SM- with a multimode (MM) fiber to describe the effect of a bigger pinhole. The
LDM600 module is used for the 635 nm experiments.
First, the highest extinction is achieved with the common procedure from chapter 3.5. After
that, the fiber connector is put directly in front of a CCD camera to image the mode (Figure
36
4. Results
4.8). If the suppression is too high, the CCD cannot capture any light. In this case, the extinction
needs to be decreased by rotating polarizer P2 until a spot is visible. One can modify the mode
inside the fiber if the laser wavelength is below the cutoff wavelength of the single-mode fiber
[17].
NA=0.95
P2
P1
Figure 4.8 Simplified setup to image different modes of the fiber and test a different sized pinhole by
replacing the SM-fiber with a MM-fiber.
First, a SM-fiber with an operating wavelength range between 620 – 820 nm (Thorlabs
PM630-HP) is used and both wavelengths achieve an ER close to 1×107 (Figure 4.9 (a)).
Secondly, the SM-fiber, which is used throughout the project, designed for a wavelength range
between 780 – 970 nm, does not alter the ER of the 905 nm experiment, but when exciting with
635 nm an ER drop of three orders of magnitude is observed (Figure 4.9 (b)). The third
experiment uses a SM-fiber with a range of 1260 – 1620 nm (Thorlabs SMF-28+), thus
exceeding both excitation wavelengths (Figure 4.9 (c)). While a cylindrical TEM01-mode for
905 nm is formed and a maximum ER of 1.4×103, the excitation with 635 nm creates a shape
similar to the rectangular TEM11-mode and a decline in ER to 3.1×105. At last, a MM-fiber
(Thorlabs AFS 105/125 Y) with an operating wavelength range of 400 – 2400 nm and a core
diameter of 105 µm is tested and the ER drops down to 70, losing five orders of magnitude
compared to the operation with a fiber at the according design wavelength and single-mode. No
real mode pattern can be observed anymore. A summary is given in Figure 4.9.
Altogether, the MM-fiber experiment with its bigger core shows that spatial filtering of the
focused beam onto the fiber is essential to achieve high extinction. The pinhole has to be at a
similar size as the focused beam. Additionally, a loss in extinction of more than three orders of
magnitude is possible, if multiple modes are present in the detection fiber. The best extinction
can only be achieved with a TEM00-mode.
37
4. Results
Laser wavelength →
635 nm
905 nm
Detection Fiber ↓
ER = 7.1×106
ER = 8.1×106
ER = 7.3×103
ER = 5×106
ER =3.1×105
ER = 1.4×103
X
ER = 70
(a) SM @ 620-820 nm
(b) SM @ 780-970 nm
1
(c) SM @ 1260-1620 nm
2
(d) MM @ 400-2400 nm
Figure 4.9 Mode dependence at two different wavelengths (635 nm, 905 nm) and comparison with a
multimode fiber. The average ER is stated above every mode image.
1
2
Cylindrical TEM01-mode (source: http://en.wikipedia.org/wiki/Transverse_mode)
Rectangular TEM11-mode (source: http://en.wikipedia.org/wiki/Transverse_mode)
38
4. Results
4.2 Mode Imaging
Working at high ER requires the knowledge of modes within the system, since these may
have severe influence on the performance. Different configurations are tested and compared to
the corresponding ER.
The high-NA sample objective is a common component in the system used to focus the
laser light and collect the light as much as possible from the emission. Two different
experiments show the behaviour and pattern of this free beam mode. First, an image of the beam
is captured after it passes the analyzer. The result in Figure 4.10 (b) shows a pattern similar to
the shape of a cloverleaf with four lobes. When additional polarization optics (QWP/LCVR)
are added, this pattern can only be retained, when the fast or the slow axis are parallel to the s
or p-polarization.
P2
NA=0.95
P1
(a)
(b)
Figure 4.10 Mode imaging of the free beam after the analyzer. (a) Setup; (b) Captured mode with lobe
pattern.
Afterwards, an imaging lens, focused to infinity, is inserted in front of the camera to get a
better view of the pattern (Figure 4.11 (a) & (b)). This lobe-pattern is only observed with the
high-NA objective; otherwise, a round spot is visible. Thus, the sample objective transforms a
small part of the linearly polarized excitation laser into the orthogonal polarization in a higher
mode. This is due to internal reflections phenomenon at the surface in the highly focused beam
that lead to a phase shift between incident and reflected wave [18]. In addition, Figure 4.11 (c)
shows a round spot for the co-polarized state.
NA=0.95
P2
imaging
lens
P1
(a)
(b)
(c)
Figure 4.11 Mode imaging of the free beam after the analyzer with an imaging lens. (a) Setup; (b) Crosspolarized; (c) Co-polarized.
Another experiment shows the evolution of this pattern in Figure 4.12 depending on the
polarization axis with respect to the plane of the beam splitter. At Δα = 0°, where delta alpha
39
4. Results
equals the rotation angle for optimum suppression, as the polarizers are perpendicular to each
other. The cloverleaf shape is also visible for low ER.
Therefore, the implemented optics alter the beam pattern and need to be taken into account.
If other components are introduced or replaced, it is recommendable to check on the behaviour
of the mode. This may lead to change in performance and specification.
Δα = 0°
Δα = 4°
Δα = 14°
Δα = 24°
Δα = 44°
Δα = 64°
Figure 4.12 Evolution of lobe-pattern dpending on the rotation angle of the poalizer P1.
4.3 Angular sensitivity of a mirror / Focus shift
Determination of the mechanical tolerance is an essential part in characterizing a new
design. This experiment analyses the effect of a shifted focus on the fiber, which is directly
connected to the mirror tilt as will be excplained. In order to find out the dependency between
mirror tilt and the extinction ratio a thorough investigation is performed comparing different
tilt axes and the behaviour of the system with and without the sample objective.
The fine adjustment screws on the mirror mount (Thorlabs KCB1E) do not come with a
distance or rotation scale, but only provide the pitch size of the screw in terms of threads per
inch or turns per inch (TPI). The µm screw used in the mirror mount has 100 TPI, which means
that 100 full turns are necessary to pass 1 inch in distance. With this information it is possible
to calculate the tilt of the mirror using the small angles approximation:
x
(1.19)
d
with x being the additional length of the tiltscrew that sticks out of the mirror base plate, d=31.2
sin   
mm being the distance of the tilt screw from the rotation point and α the tilt angle. In Figure
4.13 the mirror is represented by the white bar, the dashed shape shows the tilted mirror.
40
4. Results
x
α
d
Figure 4.13 Schematic of mirror tilt represented by the change in angle α caused by the displacement x from
the µm screw at the top.
It is not possible to measure the distance x, but one can calculate the conversion factor af
between the rotation of the screw and the mirror tilt. One complete turn of the adjustment screw
corresponds to a translation x1 of 1⁄100 inch or 254 µm. The conversion factor af is then given
by
x
sin 1  1 
 d   1.296 mrad
(1.20)
af 
rad
2
In order to monitor the rotation of the µm screw and determine its angle, a picture is taken of
every position with an Allen key stuck in the screw, while measuring the detection voltage.
Figure 4.14 shows an exemplary image of a yaw-rotation measurement. Every image is
analyzed in Microsoft Paint to calculate the angle of the Allen key using a fixed point M, which
is the middle of the adjustment screw itself and the ending of the Allen key A. For this purpose
the x,y pixels are taken from the first image of each series of measurements to find out the
length of the Allen key and afterwards calculate its relative rotation to the first position with an
Microsoft Excel routine and pixel value of every shot.
pitch
rotation
A (Ax, Ay)
M (Mx, My)
yaw
rotation
yaw+pitch
rotation
Figure 4.14 Sample screenshot and description of the setup for determing the angular sensitivity of the
mirror.
41
4. Results
Two series are performed for each rotation movement, one in the co-polarized state that
shows the decrease in fiber coupling due to misalignment or mirror tilt and the second in the
cross-polarized state that analyzes the progress of the extinction relative to the mirror tilt. The
procedure is the same for both experiments. First, the point of highest throughput for the former
experiment or highest suppression for the latter series, respectively, must be found. This is the
reference point for the mirror tilt. Then, the key is rotated slightly upwards until the voltage
changes by approximately three orders of magnitude and the measurements can start. One has
to be careful to perform the series only in downwards rotation of the key, since there is a
considerable margin between the Allen key and the adjustment screw. This way one determines
the required mechanical stability of the mirror and analyzes the focus shift that occurs at the
fiber at the same time. The schematic in Figure 4.15 shows the relation between mirror tilt α
and the focus shift Δfs in the detection arm, with the Olympus PLN10x objective, that is
calculated from
fs  f tan  2 
(1.21)
with the focus length of the objective, f.
f = 18
focus shift
Δfs
d
2α
α
NA = 0.25
Figure 4.15 Schematic drawing of the resulting focus shift after the objective, due to mirror tilt.
The terms pitch and yaw are additionally described and visualized in Figure 4.16.
pitch
pitch
+ yaw
yaw
Figure 4.16 Visual description of rotation terms at the example of the beam shape with sample objective.
The first three graphs in Figure 4.17 show the results for the (a) yaw, (b) pitch and (c)
pitch+yaw series of measurements without the sample objective. Focus shift and mirror tilt are
42
4. Results
related according to equation (1.21) and the extinction ratio is always calculated relative to the
maximum throughput, or P_max in this case. The sample objective was added afterwards to
yield the results in Figure 4.18. The test procedure and evaluation is the same.
For the first experiment, All tested axes show a quite similar behaviour, indicating a simple,
symmetric and round spot. Only the part between the two local minima is of significance for
the ER. The amount of misalignment and focus shift leads to a considerable loss in detection.
This low power is reflected in an increasing extinction ratio, which is deceptive, because the
same value for P_max is used for every point. The average ER minimum is at a mirror tilt of
0.08 mrad or a focus shift of 2.9 µm that is followed by an ER decline of up to two orders of
magnitude.
Whereas the shape for the configuration with the sample objective of the normalized power
in the co-polarized position is very similar to the previous experiments (red dashed line), the
behaviour of the extinction ratio does not show a simple behaviour anymore. Considering
Figure 4.16 of the mode image one might expect the yaw and pitch axis to show a similar
pattern. However, the pitch axis has a third local minimum, close to the point of maximum
extinction and the yaw + pitch rotation shows a distorted progress towards both sides of the
extinction maximum. The mode may be modified when focused on the fiber core. It is not clear
what exactly happens at the point of focus. A precise reconstruction of the mode with this
technique is not possible, because of the limited resolution of the tilt angle. Further ER peaks
cannot be resolved. Yet, higher sensitivity can be observed, leading to a bigger decline in ER
at similar focus shifts of the previous experiment.
43
4. Results
-0,3
-0,18
Mirror tilt [m rad]
-0,06
0,06
0,18
0,3
0,42
1E+08
0,8
1E+07
0,6
1E+06
0,4
1E+05
0,2
1E+04
0
Extinction Ratio
(a) Yaw axis.
P_max, normalized
-0,42
1
1E+03
-15
-10
-5
0
5
10
15
Focus shift [µm]
-0,3
-0,18
Mirror tilt [m rad]
-0,06
0,06
0,18
0,3
0,42
1E+08
0,8
1E+07
0,6
1E+06
0,4
1E+05
0,2
1E+04
0
Extinction Ratio
(b) Pitch axis.
P_max, normalized
-0,42
1
1E+03
-15
-10
-5
0
5
10
15
Focus shift [µm]
-0,3
-0,18
Mirror tilt [m rad]
-0,06
0,06
0,18
0,3
0,42
1E+08
0,8
1E+07
0,6
1E+06
0,4
1E+05
0,2
1E+04
0
Extinction Ratio
(c) Yaw +
pitch axis.
P_max, normalized
-0,42
1
1E+03
-15
-10
-5
0
5
10
15
Focus shift [µm]
Figure 4.17 Comparison of normalized maximum power and extinction ratio to focus shift and mirror tilt
for a setup without sample objective for different axes; (a) Yaw axis; (b) Pitch Axis; (c) Yaw + pitch axis.
44
4. Results
-0,3
-0,18
Mirror tilt [m rad]
-0,06
0,06
0,18
0,3
0,42
1E+08
0,8
1E+07
0,6
1E+06
0,4
1E+05
0,2
1E+04
0
Extinction Ratio
(a) Yaw axis.
P_max, normalized
-0,42
1
1E+03
-15
-10
-5
0
5
10
15
Focus shift [µm]
-0,3
-0,18
Mirror tilt [m rad]
-0,06
0,06
0,18
0,3
0,42
1E+08
0,8
1E+07
0,6
1E+06
0,4
1E+05
0,2
1E+04
0
Extinction Ratio
(b) Pitch axis.
P_max, normalized
-0,42
1
1E+03
-15
-10
-5
0
5
10
15
Focus shift [µm]
-0,3
-0,18
Mirror tilt [m rad]
-0,06
0,06
0,18
0,3
0,42
1E+08
0,8
1E+07
0,6
1E+06
0,4
1E+05
0,2
1E+04
0
Extinction Ratio
(c) Yaw + pitch
axis.
P_max, normalized
-0,42
1
1E+03
-15
-10
-5
0
5
10
15
Focus shift [µm]
Figure 4.18 Comparison of normalized maximum power and extinction ratio to focus shift and mirror tilt
for a setup with high-NA sample objective for different axes; (a) Yaw axis; (b) Pitch Axis; (c) Yaw + pitch
axis.
45
4. Results
4.4 Stability
It is important that the stability of the system exceeds the average time of an experiment.
The ER is monitored over a period of multiple hours at different configurations. The common
setup is drawn in its simplified version in Figure 4.19. It includes both polarizers and the sample
objective.
P2
NA=0.95
P1
Figure 4.19 Simplified setup for long-term stability test.
The first observation in Figure 4.20 is a decline in ER of about two orders of magnitude
within two hours. After this, it has a 20% increase within approximately 8 hours. A similar
increase was only observed once. No further long-term stability measurement shows this
behaviour and thus is neglected. When rotating analyzer P2 after the experiment a 50% loss in
Umax is detected. Considering the results in Figure 4.18 one can see that this loss in Umax may
indeed lead to the decline in ER, when looking at the normalized maximum voltage and the
corresponding ER.
Extinction Ratio
1E+08
1E+07
1E+06
1E+05
0
5
10
15
20
25
Time [h]
Figure 4.20 Long-term stability, with sample objective.
The sensitivity of the sample objective is much higher than the objective from the
excitation and detection arm. Small displacements of this high-NA objective lead to a drop in
ER of multiple orders of magnitude. Additionally, the impact of misaligning the mirror was
shown and quantified in chapter 4.3 that also matches the ER decrease in the stability
measurement as already mentioned. In order to observe the influence of the mirror mounting,
the sample objective is removed and both polarizers put in vertical (throughput) position. The
result (Figure 4.21) varies less than 3% within almost 14 hours, thus excluding rotation changes
46
4. Results
from the polarizer or misalignment from the mirror mounts and putting emphasis on the sample
objective.
1
U_det [V]
0,8
0,6
0,4
0,2
0
0
2
4
6
8
10
12
14
Time [h]
Figure 4.21 Long-term pointing stability without sample objective. Polarizer and analyzer are in vertical
position. The detected voltage is normalized.
Further ER experiments with and without the sample objective were still not consistent.
The detector operates at its gain limits, but a noise experiment excludes it from a measurement
error. Furthermore, temperature impact is tested with a hot air gun pointed on either polarizer
or mirror mount, without a significant long-term change.
The thin film beam splitter is then replaced with a cubic beam splitter (Thorlabs BS020).
Other tests have already shown no influence of the beam splitter to the stability or ER. An extra
5 m patch cord cable is added to eliminate potential side modes from the fiber. Again,
measurements are not fully consistent, but this configuration with two polarizers, beam splitter
cube and longer fiber cable yields the highest ER measured with a value of about 2×108 seen in
the first hour from Figure 4.22.
By the end of the project the cause for this ER decline over time could not be pinned down.
It is still suggested, that a mechanical component is responsible for the instability that does not
always cause a drop in pointing stability.
47
4. Results
Extinction Ratio
1E+09
1E+08
1E+07
1E+06
1E+05
0
2
4
6
8
10
12
14
Time [h]
Figure 4.22 Long-term stability with beam splitter cube, extra 5 m patch cord cable, no sample objective.
Highest extinction ratio of >1E8.
48
5. Summary
5. Summary
The project started with an idealized schematic of a confocal microscope, as it is used for
instance, in quantum dot measurements. It is divided into three blocks, the excitation, detection
and sample arm that are all connected with a beam splitter. It is compared to the configuration
of the confocal microscope attoCFM I head, which is designed after a multi-level principle.
These levels consist of blocks for the excitation, detection and inspection channels, all
connected via beam splitters that are mounted on the cryostat. The channels are fiber coupled
with FC/APC connectors and collimated inside the head. The beam is collimated throughout
the complete inner setup. It propagates inside the cryostat chamber until it is focused on the
sample, which is fixed on a stack of coarse and fine xyz-positioners.
The excitation and detection arm are adapted in configuration and components to create a
copy of the attoCFM I design on the breadboard. The sample arm is realized through a simple
mirror and a high-NA objective. High priority was set to a compact and stable design to reduce
the impact of vibrations and keep the configuration as close to the original attoCFM I design as
possible. In general, the choice of further components needs to be cost efficient, yet a polarizer
is chosen with a specified extinction ratio of 1×108 at the desired wavelength of 905 nm.
Another intention of the thesis is to provide a thorough description of the setup to allow
anybody who joins the project to fully understand and especially reproduce the results or extend
measurements as fast as possible. Therefore, emphasis is put on the alignment procedure that
describes a method for collimating the beam with the “beam walk” technique and effectively
couple the laser into the fiber. A working procedure explains exactly how to, practically,
achieve the highest extinction ratio. In order to fulfil this, the orientation of the polarization axis
of a polarizer is essential. A method is presented to determine the polarization axis of an
unknown polarizer by using a polarizing beam splitter cube with given specifications.
First, the coupling efficiency of the excitation and detection unit is described and measured.
Combined with further transmission measurements, which all agree with the given
specifications, a full setup efficiency, including both polarizers at parallel orientation, of 5% is
established. In order to achieve the goal of an extinction ratio of at least 1×106 a mathematical
approach proves the required resolution of the polarizer rotation mounts based on Malus’ law,
which is set to be ± 0.06° and thus feasible with the usage of the fine adjustment screw of the
Thorlabs PRM1/M rotation mount. The extinction ratio is then tested under different conditions
and implementation of different components. The results vary from 3.5×106 up to 8×107 for
different configurations, thus all fulfil the main goal. However, no improvement in extinction
could be achieved by the introduction of a tunable retarder that was supposed to correct potential
ellipticities caused by optical components. The necessity of a single-mode fiber as a pinhole
and the decline in extinction due to higher modes within the detection fiber of up to three orders
49
5. Summary
of magnitude is shown, as well as the drop of extinction of five orders of magnitude due to a
bigger core of the multi-mode fiber. A cloverleaf lobe-pattern is observed in the free beam with
the introduction of a high-NA sample objective. It is suggested that phase changes occur at the
surface of a highly focused beam that also lead to polarization changes into a higher mode. The
impact of the sample objective is also obvious in the measurement of the angular sensitivity of
the mirror in the detection arm. On average a mirror tilt of 0.08 mrad, which equals a focus shift
of 2.9 µm on the fiber, results in a decline in extinction of about two orders of magnitude. The
behaviour with the sample objective is more obscure due to the lobe pattern and shows bigger
decline in ER at similar focus shifts. During the stability measurements, a decline in ER of
about two orders of magnitude is observed and different setups tested. One configuration with
a longer excitation fiber and a different beam splitter cube achieves the highest ER of 2×108 to
date. The stability issue has been pinned down after the completion of the thesis to the sample
mirror holder.
Now, as the first goal has been achieved the next step would be to conduct an application
example, like the characterization of Stokes-vectors of the setup. It is also recommended to
implement this configuration into an existing attoCFM I head, obtain a sample and perform a
resonant fluorescence measurement.
50
BIBLIOGRAPHY
[1]
G. Wrigge, I. Gerhardt, J. Hwang, G. Zumofen, and V. Sandoghdar, “Efficient
coupling of photons to a single molecule and the observation of its resonance
fluorescence,” Nat Phys, vol. 4, no. 1, pp. 60–66, Jan. 2008.
[2]
D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vučković,
“Resonant Excitation of a Quantum Dot Strongly Coupled to a Photonic Crystal
Nanocavity,” Physical Review Letters, vol. 104, no. 7, p. 073904, Feb. 2010.
[3]
J. G. Fujimoto and D. L. Farkas, Biomedical Optical Imaging. New York: Oxford U.P,
2009.
[4]
W. Demtröder, Experimentalphysik 2 - Eletktrizität und Optik, Third. Berlin: Springer,
2004.
[5]
V. Prasad, D. Semwogerere, and E. R. Weeks, “Confocal microscopy of colloids,”
Journal of Physics: Condensed Matter, vol. 19, no. 11, p. 113102, Mar. 2007.
[6]
M. Griot, “Gaussian Beam Optics - CVI Melles Griot 2009 Technical Guide,”
Albuquerque, NM, 2009.
[7]
V. G. N. and A. V Nesterov, “Influence of beam polarization on laser cutting
efficiency,” Journal of Physics D: Applied Physics, vol. 32, no. 13, p. 1455, 1999.
[8]
N. Focus, “Polarization and Polarization Control, Application Note 3.”
[9]
F. Träger, Springer Handbook of Lasers and Optics. New York: Springer, 2007.
[10] A. Kumar and A. Ghatak, Polarization of light with Applications in Optical Fibers.
Bellingham, WA: SPIE, 2011.
[11] I. Kenyon, The light fantastic: a modern introduction to classical and quantum optics.
New York: Oxford U.P, 2008, p. 653.
[12] E. Hecht, Optics, 4th ed. San Francisco, CA: Addison Wesley, 2002.
[13] Thorlabs, “Mounted Achromatic Wave Plates.” [Online]. Available:
http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=854.
[14] K. Iizuka, Elements of Phonotics Volume I, vol. I. New York: Wiley, 2002.
[15] T. Erdogan, “A New Class of Polarization Optics Designed Specifically for Lasers,”
Rochester, NY, 2013.
[16] Thorlabs, “LPVIS050 - Ø12.5 mm Unmounted Linear Polarizer,” 2013. [Online].
Available: http://www.thorlabs.com/thorproduct.cfm?partnumber=LPVIS050.
[Accessed: 12-Mar-2013].
[17] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. Hoboken, New
Jersey: John Wiley & Sons, Inc., 2007.
51
[18]
L. Novotny, R. D. Grober, and K. Karrai, “Reflected image of a strongly focused
spot.,” Optics letters, vol. 26, no. 11, pp. 789–91, Jun. 2001.
52
ACKNOWLEDGMENT
First, I thank my supervisor Prof. Dr. Rolf Heilmann, together with my second supervisor Prof.
Dr. Manfred Fickenscher, for accepting my thesis and thus giving me the ability to successfully
finish my studies at the HS München. Much obliged is the support from Dr. Khaled Karrai on
the topic of the thesis and further discussions that taught me how to think outside the box and
to dare questioning current technological boundaries or methods. A great thank you goes to Dr.
Elena Kammann, who highly supported me at the setup and helped with the analysis and
understanding of the polarization phenomenon. Another big thank you to Klaus Thurner, who
kept me good company in the office, especially during the evening hours. Last but not least, my
heartfelt thanks to the complete staff of attocube, who were extremely helpful und supportive
throughout the whole time.
53
Name
Daniel Stroh
Geburtstag
Matrikelnummer
06POM
18.04.1985
15245106
SS 2013
Erklärung
gemäß § 13 Abs. 5 RaPo
Hiermit erkläre ich, dass ich die Masterarbeit selbstständig verfasst, noch nicht anderweitig für
Prüfungszwecke vorgelegt, keine anderen als die angegebenen Quellen oder Hilfsmittel
benützt sowie wörtliche und sinngemäße Zitate als solche gekennzeichnet habe.
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